Atkin-Lehner |
2- 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448cp |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-12280707219456 = -1 · 216 · 38 · 134 |
Discriminant |
Eigenvalues |
2- 3+ -3 4 4 13+ 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-21857,-1247871] |
[a1,a2,a3,a4,a6] |
j |
-616966948/6561 |
j-invariant |
L |
2.3543783380278 |
L(r)(E,1)/r! |
Ω |
0.19619819483619 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32448bo1 8112o1 97344fu1 32448cn1 |
Quadratic twists by: -4 8 -3 13 |